PDF Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

Description Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40)

In nonparametric and high-dimensional statistical models, the classical Gauss-Fisher-Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is then presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In the final chapter, the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions.

Mathematical Foundations of Infinite-Dimensional Statistical Models: 40 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 40) PDF ePub

Mathematical Foundations of Infinite-Dimensional ~ This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, on approximation and wavelet theory, and on the basic theory of function spaces.

Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models (Cambridge Series in Statistical and Probabilistic Mathematics Book 40) - Kindle edition by Giné, Evarist, Nickl, Richard. Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Mathematical Foundations of Infinite-Dimensional .

Mathematical Foundations of Infinite-Dimensional ~ Mathematical Foundations of Infinite-Dimensional Statistical Models. by Evarist Giné,Richard Nickl. Cambridge Series in Statistical and Probabilistic Mathematics (Book 40) Thanks for Sharing! You submitted the following rating and review. We'll publish them on our site once we've reviewed them.

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